PURPOSE: We have shown (ARVO 2001) that some simple cells in striate cortex of cat have space-time response domains whose orientation changes across space. This implies that the optimal stimulus for these cells is an accelerating or decelerating bar moving broadside. Here we propose a possible mechanism for this selectivity and compare model measurements with those of measured cells. METHODS: We modulated luminances at 16 receptive field positions, simultaneously and independently with 3-level “white noise”. We computed linear space-time responses and 2-bar nonlinear interactions from extracellular responses. We also modeled the linear responses of cells showing acceleration or deceleration selectivity by choosing two inseparable filters from a motion energy model, but with different slopes in the upper and lower regions of the receptive field. We tested both simple cells and models with a stimulus array of mean-velocities vs delta-velocities that covered a wide range of accelerations and decelerations. RESULTS: A simple model with two velocity selective subunits, each followed by a soft threshold, was capable of mimicking the linear selectivity of a cell for accelerating or decelerating stimuli. Whether the model preferred acceleration or deceleration depended on the spatial order of the subunits. When 2-bar interactions were computed for the two models with different spatial order, each model showed the same selectivity as in two simple cells each that preferred acceleration or deceleration. Selectivity for acceleration or deceleration agreed between the linear and nonlinear measures of both models and cells. CONCLUSIONS: A possible mechanism for decoding shape from motion in single cortical cells is for a receptive field to have a small number of subunits with progressive differences in preferred velocity across space. Even two subunits capture both the linear and nonlinear signature of some simple cells in responding to accelerating or decelerating stimuli.